Experimental Measurement of Vapor Pressures and Densities of Pure

May 17, 2010 - This has forced the refrigeration industry (domestic, cars, heat ... The GWP of HFP is 0.86,(2) which is negligible in comparison with ...
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J. Chem. Eng. Data 2010, 55, 2093–2099

2093

Experimental Measurement of Vapor Pressures and Densities of Pure Hexafluoropropylene Christophe Coquelet,†,‡ Deresh Ramjugernath,*,‡ Hakim Madani,§ Alain Valtz,† Paramespri Naidoo,‡ and Abdeslam Hassen Meniai§ Mines ParisTech, Centre Energe´tique et Proce´de´s, CEP/TEP 35 Rue Saint Honore´, 77305 Fontainebleau, France, Thermodynamics Research Unit, School of Chemical Engineering, University of KwaZulu-Natal, Durban, 4041, South Africa, and Laboratoire de L’inge´nierie des Proce´de´s D’environnement, Universite´ Mentouri Constantine, Alge´rie

Hydrofluoroalkenes, like hexafluoropropylene, can be considered as new fluids for refrigeration systems, and consequently volumetric and critical property data are required. In this study a vibrating-tube densitometer technique was used to determine densities at 10 different temperatures between (263 and 362) K and pressures between (0.0009 and 10) MPa. The experimental uncertainties are ( 0.0005 MPa for pressure, ( 0.02 K for the temperature, and ( 0.05 % for vapor and liquid densities. Critical properties have been determined by direct measurement and utilization of experimental densities considering scaling laws. The Wagner, Span and Wagner, Peng-Robinson, and translated Peng-Robinson equations of state are used to correlate the data.

Introduction Because of their global warming potential (GWP), hydrofluorocarbons (HFCs) will probably soon be phased out. Historically, they were used because of their zero ozone depletion potential (ODP). Prior to their use, chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) were used, but research indicated that they led to damage of the Earth’s ozone layer, and they were ultimately banned. HFCs, which do not contain chlorine, pose no threat to the ozone layer, but due to their high stability, they have a high GWP (for example, the GWP of R134a is 13001). This has forced the refrigeration industry (domestic, cars, heat pumps) to consider and find alternate HFCs which have a much lower GWP. One solution could be the utilization of hydrofluoroalkenes, like hexafluoropropene (HFP, R1216, CAS Number 116-15-4). The GWP of HFP is 0.86,2 which is negligible in comparison with the GWP of R134a. In this paper, a complete study of volumetric properties of pure HFP determined using the vibrating-tube densitometer technique3 is presented. Pure component vapor pressures were also measured and critical properties determined from these and density measurements. The Span-Wagner,4 Peng-Robinson5 (PR EoS), and volume-translated Peng-Robinson6 equations of state were used to correlate the density data.

Experimental Section Vapor-Pressure Apparatus. A classical static sapphire tube cell was used for the determination of pure HFP vapor pressures. It is similar to the cell used by Coquelet et al.7 Temperatures are measured by two Pt100 probes connected to a HP34970A data acquisition unit. These Pt100 probes were periodically calibrated against a 25 Ω reference thermometer (Tinsley Precision Instrument) certified by the Laboratoire National * Corresponding author. E-mail: [email protected]. Telephone: +27 (0) 31 260 3128. Fax: +27 (0) 31 260 1118. † Mines ParisTech, Centre Energe´tique et Proce´de´s, CEP/TEP. ‡ University of KwaZulu-Natal. § Universite´ Mentouri Constantine.

d’Essais (Paris, France). The resulting uncertainties on temperature measurements are within ( 0.02 K. Pressures were measured using a pressure transducer (model: Druck PTX611) with a pressure range of (0 to 4) MPa. The pressure transducer was calibrated against a dead weight pressure balance (model: Desgranges & Huot model 5202S) which has a (0.3 to 40) MPa pressure range. The pressure transducer is connected to the HP34970A data acquisition unit. The resulting uncertainties in pressure measurements are within ( 0.0005 MPa. Vibrating-Tube Densimeter Apparatus. A detailed description of a typical vibrating-tube density measurement apparatus is given in a previous publication (Bouchot and Richon3). The apparatus used in this work uses an Anton Paar DMA 512 vibrating tube. The vibrating tube is made of stainless steel and can work at pressures up to 40 MPa. The period of the vibration, τ, is recorded with a HP53131A data acquisition unit. The uncertainty of the vibrating period values is ( 10-8 s. The temperature of the vibrating tube is controlled by a regulated liquid bath (model: Lauda RE206) with a stability within ( 0.01 K. The temperature of the remaining parts of the circuit is regulated by a liquid bath (model: West P6100). Temperatures are measured by two Pt100 probes connected to the HP34970A data acquisition unit. These Pt100 probes are also periodically calibrated against a 25 Ω reference thermometer (model: Tinsley Precision Instrument) certified by the Laboratoire National d’Essais (Paris, France). Vacuum was achieved by means of a vacuum pump (model: AEG type LN38066008). Pressures are measured using two pressure transducers (model: Druck PTX611) with two complementary ranges: (0 to 3) MPa and (0 to 20) MPa. These sensors were calibrated against a dead weight pressure balance (model: Desgranges & Huot model 5202S) which has a (0.3 to 40) MPa pressure range and against an electronic balance (fundamental digital pressure standard, model: Desgranges & Huot 24610, France) for pressures below 0.3 MPa. The pressure transducers are connected to the HP34970A data acquisition unit.

10.1021/je900596d  2010 American Chemical Society Published on Web 05/17/2010

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Journal of Chemical & Engineering Data, Vol. 55, No. 6, 2010

Table 1. Pure Component Vapor Pressure for HFP T/K

P/MPa

T/K

P/MPa

253.26 258.26 263.16 268.24 273.24 278.21 278.22 283.23 288.21 293.19 298.22 303.22 308.21 313.21 318.22 323.20

0.1497 0.1841 0.2245 0.2720 0.3268 0.3890 0.3886 0.4590 0.5371 0.6259 0.7283 0.8397 0.9634 1.0999 1.2506 1.4135

328.21 333.21 338.18 343.21 348.22 353.23 355.24 356.24 356.76 357.06 357.27 357.47 357.56 358.26 358.76

1.5951 1.7914 2.0079 2.2438 2.5005 2.7823 2.9030 2.9653 2.9985 3.0175 3.0310 3.0442 3.0504 3.0951 3.1281

Materials. HFP was supplied by NECSA (South African Nuclear Energy Corporation) with a certified purity higher than 0.9999 volume fraction. Gas chromatographic analysis of the sample indicated a single component peak and therefore qualitatively verified the purity. Experimental Procedure. Details concerning the experimental procedure are fully described in previous papers.3 As it is a dynamic method, we take care by reducing the flow close to the critical point to cancel the effect of fluctuations of the state variable in this region. The forced path mechanical calibration model (FPMC method) proposed by Bouchot and Richon8 is used to convert periods into density values. FPMC parameters were calculated from data (PVT) of a reference fluid (R134a), whose thermodynamic properties are well-described by the equation of state of Tillner-Roth and Baehr.9 Estimation of Uncertainties. The total uncertainty on density data in the vapor and liquid phases is estimated to be ( 0.05 %, because of the uncertainties of the mechanical parameters used in the FPMC model. Total temperature uncertainties are estimated to be ( 0.02 K. Total uncertainties on pressure measurements after calibration are (( 0.0003 and ( 0.0006) MPa, respectively, for the sensor range (3 and 20) MPa.

Experimental Results Vapor Pressure. Table 1 shows the results for purecomponent vapor pressures. The temperature range for measurements was from (253.26 to 358.76) K. The values of critical temperature and pressure were determined by experimental means. The critical point was observed with the disappearance of the vapor-liquid interface and critical opalescence in the cell. From this observation, it was determined that TC ) (358.8 ( 0.1) K and PC ) (3.129 ( 0.001) MPa. The measured vapor-

pressure data were used to fit the parameters of the Frost-Kalkwarf10 equation (see eq 1). The average absolute relative deviation is less than 0.2 %, and the bias is -0.07 % (see Figure 1).

(

P/Pa ) exp A +

B + C ln(T/K) + D · 10-17 · (T/K)E (T/K) (1)

)

where P is the pressure, T is the temperature, and A, B, C, D, and E are adjustable parameters with values of 51.9463, -3799.9997, -4.5245, 10.1553, and 6, respectively. There exists some literature data for vapor pressure which has been previously measured by Li et al.,11 but their vapor pressure values are inconsistent with our measurements. We have undertaken measurements of vapor pressure independently on three separate occasions in our laboratories in France and South Africa and obtained the same results, using two separate samples of HFP. It is therefore our opinion that the data in literature are probably unreliable. Densities. Tables 2 and 3 present our experimental results for temperatures between (263 and 362) K. Please note that this is not the full set of data measured, but a selection of points. The full data set is available in the supplementary data file. Tables 4 shows the densities determined at saturation in the (0 to 10) MPa pressure range considering the vapor pressure and the previously measured densities. The densities at saturation were used to determine the critical properties of the pure component. Two laws can be used for the determination of critical temperature TC and critical density FC. The first is a scaling law directly related to the difference of densities between the vapor and the liquid phase (eq 2) and expressed as follows:

FL - FV ) A(T - TC)β

(2)

where β is an universal exponent constant (0.325). It is also assumed that the densities of the coexisting liquid and vapor obey the law of rectilinear diameters (eq 3) given as:

FL + FV ) B(T - TC) + FC 2

(3)

where FL (kg · m-3) and FV (kg · m-3) are liquid and vapor densities, respectively. A (kg · m-3 · K-β) and B (kg · m-3 · K) are adjustable parameters. The corresponding values are presented in Table 5, along with the critical properties of HFP (including acentric factor). The uncertainties on temperature and pressure are ( 0.1 K and ( 0.001 MPa, respectively. Figures 2 and 3 show the P-F diagram, including the critical point. Using eqs 2 and 3, one can obtain eqs 4 and 5 for the determination of vapor and liquid densities at saturation as follows:

Figure 1. Deviation between the calculated vapor pressure and the experimental one; A, Frost-Kalkwarf equation; B, Wagner equation.

Journal of Chemical & Engineering Data, Vol. 55, No. 6, 2010 2095 Table 2. Vapor Densities of HFP

Table 2. Continued

P

F

P

F

P

F

P

F

P

F

P

F

P

F

P

F

MPa

kg · m-3

MPa

kg · m-3

MPa

kg · m-3

MPa

kg · m-3

MPa

kg · m-3

MPa

kg · m-3

MPa

kg · m-3

MPa

kg · m-3

0.0009 0.0029 0.0057 0.0085 0.0093 0.0100 0.0107 0.0114 0.0144 0.0171 0.0215 0.0272 0.0328 0.0377 0.0432 0.0480 0.0494

0.03 0.15 0.35 0.55 0.61 0.66 0.71 0.79 0.96 1.17 1.40 1.83 2.25 2.61 2.95 3.31 3.40

0.0507 0.0561 0.0614 0.0667 0.0680 0.0693 0.0705 0.0713 0.0764 0.0816 0.0860 0.0910 0.0960 0.1004 0.1058 0.1107 0.1124

T/K ) 263.41 3.48 0.1142 3.85 0.1196 4.28 0.1244 4.62 0.1302 4.73 0.1318 4.82 0.1330 4.89 0.1347 4.97 0.1364 5.28 0.1432 5.72 0.1498 6.00 0.1563 6.41 0.1627 6.75 0.1686 7.07 0.1748 7.51 0.1809 7.85 0.1869 7.99 0.1884

8.06 8.49 8.88 9.28 9.44 9.50 9.61 9.79 10.31 10.80 11.29 11.79 12.22 12.73 13.22 13.66 13.77

0.1899 0.1957 0.2013 0.2069 0.2083 0.2096 0.2110 0.2123 0.2176 0.2211 0.2232

13.87 14.37 14.81 15.26 15.38 15.49 15.60 15.71 16.16 16.43 16.59

0.0008 0.0143 0.0288 0.1019 0.1407 0.1803 0.2204 0.2628 0.3221 0.3587 0.3988 0.4182 0.4658

0.029 0.737 1.442 5.291 7.318 9.389 11.538 13.844 17.107 19.177 21.420 22.524 25.243

0.4759 0.4997 0.5241 0.5451 0.6136 0.6601 0.7066 0.7525 0.8167 0.8546 0.8901 0.9248 0.9922

T/K ) 353.12 25.82 1.0237 27.22 1.0858 28.50 1.1468 30.00 1.2476 34.14 1.3303 36.92 1.4342 39.74 1.5313 42.62 1.6215 46.73 1.7051 49.09 1.7830 51.44 1.8548 53.65 1.9218 58.29 1.9901

60.42 64.72 69.00 76.44 82.80 91.01 99.10 106.97 114.65 122.06 129.26 136.34 143.83

2.0275 2.1025 2.1752 2.2584 2.3293 2.3935 2.4630 2.5404 2.6051 2.6704 2.7183 2.7448 2.7717

148.08 157.14 166.51 178.08 188.76 199.32 211.98 228.04 243.48 261.98 278.85 290.14 303.81

0.0036 0.0060 0.0098 0.0134 0.0170 0.0215 0.0263 0.0312 0.0363 0.0414 0.0464 0.0528 0.0635

0.14 0.30 0.52 0.85 0.98 1.25 1.57 1.87 2.23 2.51 2.84 3.28 3.98

0.0693 0.0812 0.0934 0.1044 0.1140 0.1236 0.1334 0.1457 0.1556 0.1651 0.1766 0.1866 0.1984

T/K ) 263.41 4.38 0.2033 5.20 0.2133 6.00 0.2233 6.69 0.2332 7.35 0.2432 8.03 0.2532 8.66 0.2630 9.54 0.2729 10.24 0.2831 10.87 0.2937 11.70 0.3084 12.42 0.3215 13.21 0.3344

13.55 14.30 14.99 15.69 16.38 17.15 17.89 18.60 19.39 20.20 21.36 22.28 23.37

0.3409 0.3539 0.3667 0.3795 0.3923 0.4050 0.4177 0.4303 0.4429 0.4544

0.0017 0.0048 0.0088 0.0125 0.0185 0.0234 0.0279 0.0323 0.0417 0.0625 0.0802 0.0992 0.1501

0.10 0.28 0.47 0.64 0.93 1.24 1.42 1.71 2.14 3.28 4.21 5.14 7.91

0.1759 0.2296 0.2828 0.3373 0.3909 0.4499 0.5112 0.5934 0.6756 0.7559 0.8447 0.9217 1.0077

T/K ) 355.27 9.29 1.0534 12.15 1.1409 15.02 1.2266 18.03 1.3145 20.91 1.4017 24.26 1.4866 27.76 1.5732 32.60 1.6585 37.50 1.7429 42.45 1.8299 48.08 1.9165 53.01 2.0055 58.71 2.0917

61.79 67.89 74.03 80.53 87.28 94.07 101.27 108.66 116.28 124.54 133.35 142.79 152.48

2.1353 2.2240 2.3125 2.3925 2.4845 2.5566 2.6452 2.7333 2.8187 2.9002

157.72 168.96 181.03 193.10 208.35 221.88 240.85 263.91 293.63 339.29

0.0024 0.0110 0.0163 0.0245 0.0336 0.0418 0.0525 0.0614 0.0683 0.0812 0.0942 0.1031 0.1164

0.14 0.59 0.86 1.40 1.94 2.46 3.04 3.61 3.99 4.80 5.64 6.18 6.95

0.1242 0.1373 0.1478 0.1637 0.1740 0.1844 0.2028 0.2164 0.2303 0.2512 0.2651 0.2822 0.2991

T/K ) 303.28 7.43 0.3090 8.36 0.3257 9.01 0.3462 9.96 0.3669 10.66 0.3875 11.32 0.4069 12.46 0.4357 13.34 0.4574 14.30 0.4777 15.74 0.5096 16.60 0.5359 17.78 0.5567 18.89 0.5875

19.54 20.70 22.19 23.58 25.04 26.42 28.54 30.13 31.60 33.97 36.01 37.70 40.14

0.5977 0.6256 0.6507 0.6705 0.6900 0.7189 0.7461 0.7741 0.7969 0.8236

0.0016 0.0063 0.0091 0.0135 0.0191 0.0251 0.0297 0.0351 0.0396 0.0695 0.1150 0.1592 0.2068

0.18 0.31 0.47 0.66 0.98 1.25 1.46 1.71 1.96 3.37 5.66 8.05 10.67

0.2327 0.2840 0.3349 0.3854 0.4450 0.5045 0.5642 0.6196 0.6779 0.7352 0.7912 0.8463 0.9007

T/K ) 357.06 11.91 0.9274 14.69 0.9804 17.44 1.0750 20.16 1.1763 23.53 1.2895 26.95 1.3723 30.41 1.4765 33.65 1.5680 37.14 1.6510 40.55 1.7189 44.03 1.7869 47.44 1.8757 50.90 1.9860

52.68 56.19 62.53 69.58 77.81 84.10 92.14 99.77 106.72 112.75 118.92 127.36 138.47

2.0389 2.1452 2.2536 2.3675 2.4758 2.5792 2.6866 2.7952 2.8967 2.9951 3.0070 3.0172

144.14 156.08 169.30 184.68 201.14 218.88 240.49 267.52 302.07 355.46 365.19 375.58

0.0070 0.0217 0.0366 0.0516 0.0661 0.0802 0.0944 0.1125 0.1267 0.1416 0.1571 0.1726 0.1881

0.29 1.12 2.07 2.99 3.74 4.49 5.41 6.44 7.23 8.08 8.98 9.88 10.76

0.1958 0.2111 0.2264 0.2414 0.2603 0.2806 0.2971 0.3139 0.3303 0.3470 0.3636 0.3800 0.3964

T/K ) 323.21 11.28 0.4044 12.24 0.4206 13.16 0.4444 14.08 0.5104 15.25 0.5556 16.35 0.5997 17.47 0.6430 18.45 0.6872 19.52 0.7355 20.58 0.7846 21.63 0.8431 22.69 0.8995 23.69 0.9536

24.26 25.28 26.88 31.18 34.31 37.33 40.40 43.61 47.22 50.99 55.34 60.25 64.78

0.9791 1.0261 1.0718 1.1207 1.1657 1.2116 1.2549 1.2987 1.3475 1.3925

0.0040 0.0058 0.0075 0.0092 0.0145 0.0196 0.0239 0.0290 0.0330 0.0391 0.0453 0.0722 0.0994

0.07 0.15 0.23 0.32 0.60 0.84 1.07 1.31 1.50 1.80 2.13 3.58 4.96

0.1155 0.1520 0.1883 0.2286 0.2816 0.3375 0.3962 0.4604 0.5253 0.5927 0.6638 0.7373 0.8086

T/K ) 358.16 5.84 0.8439 7.73 0.9123 9.64 0.9814 11.76 1.0567 14.57 1.1778 17.58 1.2775 20.78 1.3845 24.33 1.5224 28.12 1.6593 31.99 1.7809 36.18 1.9167 40.62 2.0516 44.92 2.1856

47.16 51.52 56.09 61.12 69.69 76.93 84.60 95.50 106.85 117.54 130.47 144.28 159.34

2.2505 2.3818 2.5626 2.6699 2.8063 2.9391 3.0057 3.0155 3.0258 3.0375 3.0509 3.0645 3.0770

167.24 184.60 212.61 232.45 263.68 305.79 336.23 341.83 348.17 355.40 364.96 376.75 389.78

0.0032 0.0121 0.0224 0.0320 0.0399 0.0554 0.0708 0.0801 0.0899 0.1101 0.1355 0.1609 0.1896

0.22 0.73 1.29 1.75 2.11 3.00 3.87 4.42 4.91 6.10 7.51 8.89 10.49

0.2005 0.2505 0.2983 0.3477 0.3965 0.4433 0.4909 0.5486 0.6044 0.6603 0.7156 0.7705 0.8239

T/K ) 343.26 11.16 0.8502 14.05 0.9022 16.80 0.9540 19.66 1.0082 22.56 1.0603 25.35 1.1156 28.19 1.1703 31.65 1.2311 35.15 1.2903 38.68 1.3472 42.26 1.4037 45.84 1.4587 49.41 1.5111

51.23 54.71 58.46 62.31 66.22 70.43 74.72 79.48 84.46 89.34 94.34 99.32 104.29

1.5621 1.6692 1.7733 1.8809 1.9861 2.0963 2.1724 2.2377 2.2417

0.0063 0.0172 0.0318 0.0423 0.0751 0.1031 0.1346 0.1626 0.2059 0.2617 0.3059 0.3709 0.4493

0.34 0.88 1.53 2.22 3.75 5.20 6.83 8.20 10.23 13.26 15.65 19.21 23.60

0.4851 0.5603 0.6388 0.7156 0.8092 0.8816 0.9522 1.0440 1.1197 1.2214 1.2933 1.3671 1.4479

T/K ) 362.90 25.57 1.4849 29.54 1.5678 34.15 1.6767 38.68 1.7530 44.11 1.8382 48.62 1.9536 53.09 2.0213 59.01 2.1156 63.86 2.2390 70.92 2.3206 76.00 2.3992 81.15 2.4937 86.99 2.5845

89.90 96.26 104.81 111.40 118.54 129.06 135.65 144.99 158.23 167.17 176.97 188.92 201.68

2.6376 2.7064 2.8095 2.9447 3.0328 3.1403 3.2099 3.2859 3.3779 3.4453 4.5053 4.6265 4.7078

209.57 220.44 238.50 266.58 287.81 320.42 347.93 389.23 530.57 659.79 920.24 929.99 936.10

0.0024 0.0054 0.0089 0.0170 0.0277 0.0367 0.0465 0.0626 0.0789 0.0959 0.1211 0.1516 0.1760

0.05 0.18 0.35 0.83 1.44 1.87 2.39 3.24 4.06 4.89 6.31 7.92 9.23

0.1869 0.2089 0.2452 0.2810 0.3175 0.3522 0.3865 0.4201 0.4709 0.5280 0.5912 0.6721 0.7358

T/K ) 348.12 9.89 0.7655 10.99 0.8447 13.05 0.9156 15.00 0.9858 17.06 1.0578 19.05 1.1386 20.98 1.2018 22.92 1.2651 25.92 1.3304 29.29 1.3953 33.18 1.4603 38.15 1.5401 42.16 1.6393

44.05 49.34 54.20 58.92 64.05 69.96 74.83 79.72 84.96 90.32 95.93 103.11 112.32

1.6838 1.7806 1.8729 1.9679 2.0685 2.2121 2.3102 2.3973 2.4728 2.4815 2.4901 2.4988

23.85 24.84 25.93 26.94 27.96 28.98 30.05 31.07 32.26 33.16

41.02 43.25 45.35 47.07 48.67 51.33 53.68 56.30 58.41 61.02

66.90 71.06 75.20 80.05 84.23 88.92 93.54 98.44 104.06 109.80

109.24 120.33 132.05 145.46 160.18 177.82 192.40 208.04 211.34

A(T - TC)β 2

(4)

A(T - TC)β F ) B(T - TC) + FC 2

(5)

FL ) B(T - TC) + FC + 116.62 126.81 137.09 148.35 161.51 183.28 201.01 219.85 240.22 242.88 245.80 250.42

V

Using these two equations, the average absolute relative deviations are 5.9 % and 1 % for the vapor and liquid density, respectively. The deviation is more significant for the vapor density due to its low order of magnitude. The critical parameters, TC and PC, are found to be in very good agreement with those determined through the vapor

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Journal of Chemical & Engineering Data, Vol. 55, No. 6, 2010

Table 3. Liquid Densities of HFP

Table 3. Continued

P

F

P

F

P

F

P

F

P

F

P

F

P

F

P

F

MPa

kg · m-3

MPa

kg · m-3

MPa

kg · m-3

MPa

kg · m-3

MPa

kg · m-3

MPa

kg · m-3

MPa

kg · m-3

MPa

kg · m-3

0.2302 0.2321 0.2506 0.2739 0.3272 0.3459 0.3880 0.4311 0.4841 0.5182 0.5541 0.6252 0.7283 0.7512

1462.58 1462.66 1462.76 1462.91 1463.13 1463.25 1463.45 1463.65 1463.94 1464.18 1464.39 1464.59 1465.20 1465.25

0.7721 0.8883 0.9829 1.1328 1.2832 1.4253 1.5764 1.7182 1.8735 2.0176 2.2520 2.4891 2.7334 2.7905

T/K ) 1465.47 1465.94 1466.54 1467.28 1467.96 1468.74 1469.48 1470.09 1471.02 1471.69 1472.79 1474.06 1475.13 1475.34

1475.67 1476.76 1477.91 1479.03 1480.12 1481.02 1482.25 1483.36 1484.43 1485.97 1487.53 1489.06 1490.42 1490.70

6.2924 6.6284 6.9654 7.3151 7.6630 8.0082 8.3430 8.6870 9.0334 9.3717 9.5889 9.7603 9.9337 9.9766

1491.15 1492.50 1493.98 1495.44 1496.86 1498.24 1499.65 1500.96 1502.38 1503.79 1504.56 1505.19 1505.89 1506.02

2.7984 2.8257 2.8526 2.8810 2.9482 3.0305 3.1161 3.2055 3.2863 3.3692 3.4579 3.5743 3.6804

887.06 893.67 899.46 904.67 915.77 926.96 937.73 946.93 954.54 961.77 969.07 977.54 984.80

3.7360 3.8407 3.9437 4.0667 4.2160 4.3743 4.5340 4.6920 4.8549 5.0121 5.1691 5.3253 5.4808

T/K ) 353.13 988.50 5.5598 994.81 5.7117 1000.71 5.8654 1007.14 6.0196 1014.76 6.1779 1022.01 6.3335 1028.89 6.4846 1035.33 6.6427 1041.63 6.8028 1047.29 6.9608 1052.89 7.1144 1057.82 7.2709 1062.93 7.4266

1065.32 1069.91 1074.15 1078.56 1082.78 1086.90 1090.62 1094.43 1098.22 1101.88 1105.30 1108.59 1111.94

7.5217 7.7198 7.9258 8.1280 8.3333 8.5330 8.7394 8.9409 9.1455 9.3534 9.5556 9.7623 9.9692

1113.95 1117.99 1122.03 1125.99 1129.80 1133.60 1137.27 1140.78 1144.29 1147.68 1150.83 1154.19 1157.38

1408.82 1410.42 1411.65 1413.10 1414.61 1416.66 1418.20 1419.73 1421.22 1422.82 1424.29 1425.90 1427.34

7.7803 8.0530 8.2222 8.3934 8.5634 8.7357 8.9123 9.0904 9.2610 9.4390 9.6122 9.7780 9.9911

1428.05 1429.55 1430.51 1431.32 1432.23 1433.12 1434.00 1435.02 1435.85 1436.78 1437.57 1438.42 1439.48

2.9179 2.9277 2.9369 2.9466 2.9677 3.0045 3.0399 3.1369 3.1787 3.2212 3.2731 3.3254 3.4102

845.60 849.49 852.80 855.85 861.92 872.46 880.60 897.86 904.31 910.46 917.41 923.75 933.28

3.4534 3.5605 3.6672 3.7516 3.8289 3.9389 4.0336 4.1298 4.2068 4.2818 4.4498 4.5990 4.7949

T/K ) 355.18 937.53 4.8739 947.64 5.0298 956.48 5.2368 963.12 5.3987 968.54 5.6014 976.09 5.7682 981.94 5.9355 987.54 6.1632 992.10 6.3624 995.99 6.6115 1004.57 6.8128 1011.60 7.0149 1020.36 7.2658

1023.70 1029.94 1037.65 1043.42 1050.18 1055.50 1060.51 1067.09 1072.65 1079.21 1084.30 1089.29 1095.06

7.3662 7.5663 7.8173 8.0691 8.2739 8.4785 8.6815 8.8868 9.1381 9.3393 9.5929 9.7962 9.9981

1097.33 1101.91 1107.12 1112.30 1116.30 1120.28 1124.00 1127.78 1132.17 1135.60 1139.78 1143.06 1146.19

3.0285 3.0371 3.0460 3.0629 3.0771 3.0956 3.1239 3.1738 3.2302 3.2826 3.3340 3.4004 3.4779

789.77 796.63 802.75 812.63 819.71 828.01 838.10 853.47 866.99 877.54 886.47 896.81 907.30

3.5149 3.6392 3.7401 3.8661 3.9667 4.0732 4.1551 4.2583 4.3408 4.4458 4.9706 5.1784 5.3442

T/K ) 357.01 911.85 5.4264 926.14 5.6368 936.03 5.8027 946.85 5.9664 954.74 6.2021 962.41 6.3654 967.92 6.5277 974.59 6.7306 979.70 6.8942 985.59 7.0993 1011.35 7.2652 1020.12 7.4728 1026.56 7.6376

1029.68 1037.33 1043.00 1048.43 1055.73 1060.53 1065.18 1070.82 1075.07 1080.34 1084.37 1089.26 1093.07

7.7607 7.9257 8.1340 8.3010 8.5103 8.6759 8.8848 9.0550 9.2649 9.4765 9.6409 9.8105 9.9732

1095.83 1099.42 1103.77 1107.38 1111.46 1114.70 1118.68 1121.82 1125.67 1129.45 1132.16 1135.04 1137.69

3.1167 3.1358 3.1778 3.2108 3.2522 3.3060 3.3949 3.4829 3.5720 3.6720 3.6720

777.53 792.11 815.22 828.42 841.71 855.88 874.14 888.76 901.37 913.13 913.13

3.7375 3.8493 3.9597 4.0787 4.2095 4.3778 4.4626 4.5998 4.7758 4.9107 5.0847 5.3636 5.5920

T/K ) 358.00 920.30 5.7021 931.26 5.9326 940.96 6.1492 950.34 6.3043 959.82 6.4528 970.84 6.6373 975.95 6.7843 983.70 6.9319 993.10 7.1901 999.61 7.3417 1007.62 7.5323 1019.45 7.6801 1028.23 7.8283

1032.29 1040.24 1047.34 1052.13 1056.39 1061.72 1065.78 1069.87 1076.36 1080.24 1084.80 1088.21 1091.56

7.9034 8.0561 8.2042 8.4277 8.6147 8.7628 8.9464 9.0945 9.3181 9.5060 9.6893 9.8391 9.9880

1093.29 1096.58 1099.77 1104.39 1108.07 1111.12 1114.65 1117.44 1121.42 1124.84 1128.07 1130.57 1133.16

4.7626 4.8782 4.9628 5.0808 5.2128 5.3474 5.5534 5.6935 5.8323 5.8981 5.9309

939.84 947.51 952.76 959.79 967.09 974.13 984.34 990.75 996.63 999.35 1000.69

6.0351 6.1720 6.3085 6.4472 6.5844 6.7205 6.8603 7.0297 7.1685 7.2376 7.2731

T/K ) 362.90 1005.02 7.3780 1010.25 7.5470 1015.34 7.6897 1020.30 7.8334 1025.06 7.9767 1029.53 8.1150 1034.08 8.2813 1039.21 8.4318 1043.39 8.5773 1045.38 8.6493 1046.40 8.6894

1049.33 1053.95 1057.93 1061.54 1065.12 1068.60 1072.48 1075.97 1079.34 1080.92 1081.74

8.8002 8.9375 9.0731 9.2058 9.3417 9.4794 9.6526 9.7892 9.9295 9.9965

1084.14 1087.05 1089.94 1092.74 1095.45 1098.06 1101.51 1104.04 1106.67 1107.93

263.49 2.8485 3.0933 3.3273 3.5582 3.7965 4.0109 4.2612 4.5075 4.7570 5.1048 5.4563 5.7933 6.1299 6.2108

0.4677 0.4830 0.5268 0.5740 0.6629 0.7519 0.8563 0.9456 1.0474 1.1651 1.3208 1.4635 1.6346

1382.09 1382.29 1382.57 1382.98 1383.60 1384.27 1384.98 1385.66 1386.36 1387.20 1388.36 1389.43 1390.61

1.7209 1.8950 2.0763 2.3062 2.5066 2.6840 2.9004 3.1802 3.3942 3.5914 3.8643 4.0785 4.2934

T/K ) 283.17 1391.22 4.4099 1392.44 4.6761 1393.62 4.8895 1395.23 5.1263 1396.64 5.3727 1397.73 5.7202 1399.13 5.9972 1400.96 6.2609 1402.39 6.5315 1403.66 6.8020 1405.48 7.0853 1406.71 7.3596 1408.17 7.6347

0.8517 0.8700 0.8877 0.9183 0.9434 0.9655 0.9956 1.0213 1.0634 1.1063 1.1747 1.2350 1.3056

1288.08 1288.22 1288.47 1288.76 1289.10 1289.39 1289.74 1290.00 1290.50 1291.06 1291.89 1292.43 1293.27

1.3402 1.4489 1.5403 1.6372 1.7710 1.8617 1.9856 2.1191 2.3260 2.4451 2.5852 2.8080 2.9403

T/K ) 303.36 1293.72 3.0229 1294.92 3.1503 1296.17 3.2767 1297.09 3.4014 1298.55 3.5329 1299.58 3.7996 1301.03 4.0681 1302.35 4.3849 1304.46 4.6529 1305.96 4.8618 1307.14 5.0881 1309.41 5.4787 1310.77 5.7313

1311.53 1312.98 1313.98 1315.17 1316.48 1319.05 1321.53 1324.43 1326.85 1328.62 1330.55 1333.80 1335.77

5.9216 6.1699 6.4870 6.7420 7.0538 7.3085 7.5636 7.8797 8.2906 8.7685 9.1681 9.6673 9.9926

1337.37 1339.47 1341.93 1343.99 1346.25 1348.26 1350.15 1352.39 1355.42 1358.79 1361.57 1364.90 1366.98

1.4194 1.4271 1.4457 1.4972 1.5497 1.6060 1.6653 1.7186 1.7973 1.8974 1.9888 2.1026 2.2133

1174.23 1174.45 1175.00 1176.12 1177.31 1178.65 1179.86 1180.95 1182.59 1184.74 1186.54 1188.84 1191.16

2.2771 2.3967 2.5112 2.6713 2.8332 2.9892 3.1485 3.3193 3.4943 3.6555 3.8142 3.9683 4.1259

T/K ) 323.37 1192.28 4.2039 1194.59 4.3650 1196.77 4.5108 1199.65 4.7275 1202.46 4.9384 1205.13 5.1557 1207.95 5.3860 1210.67 5.5755 1213.56 5.8081 1215.99 6.0350 1218.51 6.2654 1220.84 6.4946 1223.19 6.7214

1224.27 1226.67 1228.65 1231.69 1234.66 1237.37 1240.28 1242.70 1245.67 1248.49 1251.23 1253.91 1256.27

6.8379 7.0672 7.2995 7.5314 7.7647 7.9955 8.2779 8.5653 8.8715 9.1280 9.4048 9.6829 9.9863

1257.77 1260.31 1262.75 1265.19 1267.63 1270.08 1272.98 1275.71 1278.77 1281.22 1283.76 1286.27 1289.02

2.2571 2.2792 2.3140 2.3486 2.3867 2.4264 2.4640 2.4971 2.5568 2.6329 2.7106 2.7821 2.8522

1022.11 1024.07 1026.50 1028.71 1030.85 1032.67 1034.92 1037.07 1040.31 1044.34 1048.77 1051.54 1055.00

2.8871 2.9674 3.0782 3.2019 3.3320 3.4633 3.5866 3.7282 3.8825 4.0492 4.2269 4.4108 4.5991

T/K ) 343.18 1056.99 4.6976 1060.20 4.8874 1064.77 5.0739 1069.74 5.3019 1075.03 5.4740 1079.82 5.7021 1084.11 5.8913 1089.03 6.1600 1093.89 6.4073 1099.28 6.7259 1104.11 6.9766 1109.10 7.1637 1114.05 7.3547

1116.51 1121.18 1125.85 1130.82 1134.83 1139.38 1143.58 1148.79 1153.32 1159.01 1163.25 1166.50 1169.81

7.4775 7.6634 7.8376 8.0431 8.2915 8.4648 8.6707 8.8812 9.1234 9.3501 9.5675 9.7499 9.9626

1171.63 1174.54 1177.31 1180.22 1184.04 1186.51 1189.47 1192.40 1195.43 1198.56 1201.28 1203.76 1206.45

2.8351 2.8885 2.9691 3.0615 3.1352 3.2025 3.2870 3.3306 3.3593 3.3862 3.4508 3.6201 3.8755

T/K ) 348.16 989.69 4.0308 993.69 4.2787 999.28 4.5260 1005.54 4.7760 1009.88 5.0226 1013.88 5.2672 1018.73 5.5133 1020.95 5.7622 1022.61 6.0125 1023.86 6.2622 1027.09 6.5177 1035.16 6.7677 1046.10 7.0175

1052.17 1061.59 1070.05 1077.88 1085.31 1091.82 1098.50 1104.69 1110.68 1116.40 1121.84 1127.07 1132.05

7.1428 7.3962 7.6468 7.8977 8.1497 8.4063 8.6597 8.9117 9.1703 9.3994 9.6096 9.7889 10.0158

1134.61 1139.31 1143.93 1148.36 1152.67 1157.00 1160.84 1164.85 1168.80 1172.31 1175.39 1175.42 1180.60

2.5064 2.5107 2.5170 2.5226 2.5322 2.5423 2.5545 2.5817 2.6147 2.6547 2.7061 2.7569 2.8094

959.60 960.12 960.83 961.35 962.81 963.60 964.95 967.68 970.90 974.76 979.32 983.71 987.97

pressure measurements. Information obtained from Air Liquide Safety sheets (http://www.encyclopedia.airliquide.com/sds/fr/ 066_AL_FR.pdf) lists TC ) 359.35 K; the Dupont de Nemours Safety sheet12 lists TC ) 358.95 K. DIPPR13 states a value of TC ) 368 K. The value of TC (358.93 K) obtained in our study is in very good agreement with that listed in the Dupont de Nemours Safety sheet.

Modeling Vapor Pressure. The Wagner14 equation is used to correlate the pure-component vapor pressure (eq 6).

Journal of Chemical & Engineering Data, Vol. 55, No. 6, 2010 2097

Figure 2. HFP P-F diagram. 4, experimental densities; ×, critical point; black line, calculated densities using eqs 4 and 5. Table 4. Vapor and Liquid Densities at Saturation vapor phase

liquid phase

T

P

FV

K

MPa

kg · m-3

263.41 283.24 303.28 323.21 343.26 348.12 353.12 355.27 357.06 358.16

0.2277 0.4586 0.8389 1.4130 2.2490 2.4994 2.7794 2.9072 3.0172 3.0865

17.0 35.7 65.2 116.3 217.2 250.2 306.7 345.6 375.6 391.3

a

T

P

FL

∆FVa

K

MPa

kg · m-3

∆FLa

( 0.2 ( 0.1 ( 0.1 ( 0.2 ( 0.4 ( 0.3 ( 1.0 ( 0.2 ( 0.2 ( 0.4

263.49 283.17 303.36 323.37 343.18 348.16 353.13 355.18 357.01 358.00

0.2284 0.4576 0.8408 1.4186 2.2451 2.5016 2.7800 2.9018 3.0141 3.0763

1462.6 1382.1 1288.0 1174.2 1021.6 959.3 883.5 844.0 780.0 708.0

( 0.2 ( 0.2 ( 0.2 ( 0.3 ( 0.6 ( 0.3 ( 1.0 ( 0.5 ( 0.2 ( 0.4

Estimated uncertainty due to density determination.

( )

ln

TC p ) (A1τ + A2τ1.5 + A3τ3 + A4τ6) pC T with τ ) 1 -

(6)

T TC

Critical properties used are those obtained using our correlations (eqs 1 to 3). The data are well-correlated, and the parameters are presented in Table 6. The bias and average absolute deviation are 0.02 % and 0.08 %, respectively. The PR EoS, which is the most-used equation of state in industry, with the Mathias-Copeman (MC)15 R function was also used to correlate the vapor-pressure data. The MC parameters (c1, c2, and c3) are indicated in Table 6. The average

absolute relative deviation is less than 0.1 %, and bias is -0.01 % (see Figure 1). Densities. The Span-Wagner EoS adapted to polar fluids was used to correlate the data. We have used the densities at saturation and the corresponding vapor pressure to determine the parameters.

Aγ ) RT

12

∑ niδd τt exp(eiδp ) i

i

i

(7)

1

with τ )

TC T

and

δ)

F FC

The parameters are presented in Table 6. The PR EoS is also used to compare the densities at saturation with the densities calculated with the Span-Wagner EoS and the experimental one (see Figure 4). The Span-Wagner EoS represents with some difficulties with our experimental data (there are 12 adjustable parameters), particularly close to the critical point. Figure 5 presents the pure-component vapor pressures. It seems that more data are required to generate a good equation of state. The Span-Wagner EoS determined different property values for the critical point (TC ) 358.9 K, FC ) 589.5 kg · m-3, and PC ) 3.189 MPa). We have tested also the PR EoS on the calculation of densities (Figure 4). As expected, the PR EoS is not accurate enough to represent the densities of the liquid phase at saturation. For this reason, the PR volume-translated EoS was also used to improve the representation of the densities, and it gave reasonable representation of both the liquid and the vapor densities at

Table 5. Pure-Component Critical Properties and Mathias-Copeman r Function Parameters critical properties -3

Mathias-Copeman parameters

TC/K

PC/MPa

FC/(kg · m )

Pitzer’s acentric factor ω

ZC

c1

c2

c3

358.9

3.136

579.03

0.3529

0.27226

0.8926

-0.5100

3.1585

Eqs 4 and 5 Parameters A

B

329.47

1.73

2098

Journal of Chemical & Engineering Data, Vol. 55, No. 6, 2010

Figure 3. HFP P-F diagram. 4, experimental densities at saturation; ×, out of saturation; 362.90 K; ], 355.18 K, and 0, 303.28 K; O, critical point; black line, eqs 4 and 5.

Figure 4. HFP P-F diagram. 4, experimental densities; ×, critical point from eqs 1 to 3; O, critical point obtained with the translated PR EoS; 2, critical density obtained with the PR EoS; bold line, calculated densities with the Span-Wagner equation; black line, calculated densities using the PR EoS; dashed line, calculated using the translated PR EoS.

Table 6. Wagner and Span-Wagner Equation Parameters Wagner equation

Span-Wagner equation

i

Ai

di

ti

ei

pi

ni

1 2 3 4 5 6 7 8 9 10 11 12

-7.56784 1.31089 -5.03405 0.60477

1 1 1 3 7 1 2 5 1 1 4 2

0.25 1.25 1.5 0.25 0.875 2.375 2 2.125 3.5 6.5 4.75 12.5

0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1

0 0 0 0 0 1 1 1 2 2 2 3

1.06801 -2.69766 0.431879 0.0846552 0.00029316 0.566737 0.475546 -0.0390086 -0.447262 -0.0784903 -0.126779 0.00327112

low pressures. Concerning the calculation at high pressure, it calculated values significantly higher than the “good” expected values for both phase densities particularly at pressures in the critical region. In fact, density data and purecomponent vapor pressures were used to fit the equation of state parameters and critical properties. The estimated critical temperature and pressure are 367.20 K and 3.665 MPa, respectively. This calculation reveals that it is difficult to represent very accurately the thermodynamic properties in the vicinity of the critical point, and a specific model must be developed like those used by Anisimov and Sengers16 considering the asymptotic-scaled equation of state and renormalization theory.

Journal of Chemical & Engineering Data, Vol. 55, No. 6, 2010 2099

Figure 5. Pure HFP vapor pressure. 4, experimental data; solid line, the Span-Wagner equation of state.

Conclusion A vibrating-tube densitometer was used to determine the density of pure hexafluoropropylene. The uncertainties of the vapor and liquid densities were ( 0.05 % using the FPMC approach. Using these data, new values of critical properties were determined and validated through visual measurement on a static cell. Supporting Information Available: Vapor and liquid densities of HFP at various temperatures. This material is available free of charge via the Internet at http:// pubs.acs.org.

Literature Cited (1) McMullan, J. T. Refrigeration and the environment issues and strategies for the future. Int. J. Refrig. 2002, 25, 89–99. (2) Acerboni, G.; Buekes, J. A.; Jensen, N. R.; Hjorth, J.; Myhre, G.; Nielsen, C. J.; Sundet, J. K. Atmospheric degradation and global warming potentials of three perfluoroalkenes. Atmos. EnViron. 2001, 35, 4113–4123. (3) Bouchot, C.; Richon, D. Direct pressure-volume-temperature and vapor-liquid equilibrium measurements with a single equipment using a vibrating tube densimeter up to 393 K and 40 MPa: description of the original apparatus and new data. Ind. Eng. Chem. Res. 1998, 37, 3295–3304. (4) Peng, D. Y.; Robinson, D. B. A new two parameters Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59–64. (5) Span, R.; Wagner, W. Equations of state for technical applications. III. Results for polar fluids. Int. J. Thermophys. 2003, 24, 111–161. (6) Peneloux, A.; Rauzy, E. A consistent correction for Redlich-KwongSoave volumes. Fluid Phase Equilib. 1982, 8, 7–23.

(7) Coquelet, C.; Valtz, A.; Richon, D. Vapor - Liquid Equilibrium Data for the Difluoromethane (R32) + Dimethyl Ether (DME) System at Temperatures from 283.03 to 363.21 K and Pressures up to about 5.5 MPa. Fluid Phase Equilib. 2005, 232, 44–49. (8) Bouchot, C.; Richon, D. An enhanced method to calibrate vibrating tube densimeters. Fluid Phase Equilib. 2001, 191, 189–208. (9) Tillner-Roth, R.; Baehr, H. D. An international standard formulation for the properties of 1,1,1,2-tetrafluoroethane (HFC-R134a) for temperatures from 170 to 455 K and pressures up to 70 MPa. J. Phys. Chem. Ref. Data 1994, 23, 657–729. (10) Frost, A. A.; Kalkwarf, D. R. A semi-empirical equation for the vapor pressure of liquids as a function of temperature. J. Chem. Phys. 1953, 21, 264–267. (11) Li, C.; Feng, Y.; Wu, Z. Vapor pressure of hexafluoropropylene. J. Chem. Eng. Chin. UniV. 1996, 10, 64–66. (12) Dupont de Nemours, 2008. www.dupont.com/FluoroIntermediates/ en_US/assets/downloads/h96536.pdf. (13) Daubert, T. E.; Danner, R. P.; Sibel, H. M.; Stebbins, C. C. Physical and thermodynamic properties of pure chemicals: Taylor & Francis: Washington, DC, 1997. (14) Wagner, W. New vapour pressure measurements for argon and nitrogen and a new method for establishing rational vapour pressure. Cryogenics 1973, 13, 470–482. (15) Mathias, P. M.; Copeman, T. W. Extension of The Peng Robinson Equation of State to Complex Mixtures: Evaluation of the Various Forms of the local Composition Concept. Fluid Phase Equilib. 1983, 13, 91–108. (16) Anisimov, M. A.; Sengers, J. V. Equations of state for fluids and fluid mixtures; Elsevier: Amsterdam, The Netherlands, 2000.

Received for review July 15, 2009. Accepted April 20, 2010.

JE900596D